张新祥,吴国昌.关于Parseval框架小波的刻画[J].数学研究及应用,2011,31(2):242~250 |
关于Parseval框架小波的刻画 |
The Characterization of Parseval Frame Wavelets |
投稿时间:2009-03-17 修订日期:2009-06-30 |
DOI:10.3770/j.issn:1000-341X.2011.02.007 |
中文关键词: 伪拟尺度函数 广义低通滤波器 Parseval框架小波. |
英文关键词:generalized low pass filter Pseudo-scaling function MRA Parseval frame wavelets. |
基金项目:国家自然科学基金(Grant No.60774041),河南省教育厅自然科学基金(Grant No.2010A110002). |
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中文摘要: |
本文中,我们主要研究矩阵伸缩MRA Parseval框架小波和广义低通滤波器的刻画问题。 我们讨论了伪拟的尺度函数、广义的低通滤波器和MRA Parseval框架小波的刻画问题;进一步地,我们也给出了 半正交的MRA Parseval框架小波的一个刻画。 |
英文摘要: |
In this paper, we characterize all generalized low pass filters and MRA Parseval frame wavelets in $L^2(R^n)$ with matrix dilations of the form $(D f )(x) = \sqrt{2}f (Ax)$, where $A$ is an arbitrary expanding $n\times n$ matrix with integer coefficients, such that $|{\rm det}\,A| =2$. We study the pseudo-scaling functions, generalized low pass filters and MRA Parseval frame wavelets and give some important characterizations about them. Furthermore, we give a characterization of the semiorthogonal MRA Parseval frame wavelets and provide several examples to verify our results. |
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